| 书目名称 | The Geometry of Walker Manifolds |
| 编辑 | Miguel Brozos-Vázquez,Eduardo García-Río,Ramón Váz |
| 视频video | |
| 丛书名称 | Synthesis Lectures on Mathematics & Statistics |
| 图书封面 |  |
| 描述 | This book, which focuses on the study of curvature, is an introduction to various aspects of pseudo-Riemannian geometry. We shall use Walker manifolds (pseudo-Riemannian manifolds which admit a non-trivial parallel null plane field) to exemplify some of the main differences between the geometry of Riemannian manifolds and the geometry of pseudo-Riemannian manifolds and thereby illustrate phenomena in pseudo-Riemannian geometry that are quite different from those which occur in Riemannian geometry, i.e. for indefinite as opposed to positive definite metrics. Indefinite metrics are important in many diverse physical contexts: classical cosmological models (general relativity) and string theory to name but two. Walker manifolds appear naturally in numerous physical settings and provide examples of extremal mathematical situations as will be discussed presently. To describe the geometry of a pseudo-Riemannian manifold, one must first understand the curvature of the manifold. We shall analyze a wide variety of curvature properties and we shall derive both geometrical and topological results. Special attention will be paid to manifolds of dimension 3 as these are quite tractable. We then |
| 出版日期 | Book 2009 |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-031-02397-2 |
| isbn_softcover | 978-3-031-01269-3 |
| isbn_ebook | 978-3-031-02397-2Series ISSN 1938-1743 Series E-ISSN 1938-1751 |
| issn_series | 1938-1743 |
| copyright | Springer Nature Switzerland AG 2009 |
发表于 2025-3-21 18:19:02
